Tutorial 2 FORECASTING

OPERATIONS MANAGEMENT

What is Forecasting?

► Process of predicting a future event

► Underlying basis of all business decisions

► Production► Inventory► Personnel► Facilities

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1. Short-range forecast► Up to 1 year, generally less than 3 months► Purchasing, job scheduling, workforce levels,

job assignments, production levels

2. Medium-range forecast► 3 months to 3 years► Sales and production planning, budgeting

3. Long-range forecast► 3+ years► New product planning, facility location,

research and development

Forecasting Time Horizons

Distinguishing Differences

1. Medium/long range forecasts deal with more comprehensive issues and support management decisions regarding planning and products, plants and processes

2. Short-term forecasting usually employs different methodologies than longer-term forecasting

3. Short-term forecasts tend to be more accurate than longer-term forecasts

Influence of Product Life Cycle

► Introduction and growth require longer forecasts than maturity and decline

► As product passes through life cycle, forecasts are useful in projecting

► Staffing levels► Inventory levels► Factory capacity

Introduction – Growth – Maturity – Decline

Product Life Cycle

Best period to increase market share

R&D engineering is critical

Practical to change price or quality image

Strengthen niche

Poor time to change image, price, or quality

Competitive costs become criticalDefend market position

Cost control critical

Introduction Growth Maturity Decline

Com

pany

Str

ateg

y/Is

sues

Figure 2.5

Internet search engines

Sales

Drive-through

restaurantsDVDs

Analog TVs

Boeing 787

Electric vehicles

iPods

3-D game players

3D printers

Xbox 360

Types of Forecasts

1. Economic forecasts► Address business cycle – inflation rate, money

supply, housing starts, etc.

2. Technological forecasts► Predict rate of technological progress► Impacts development of new products

3. Demand forecasts► Predict sales of existing products and services

Forecasting Approaches

► Used when situation is vague and little data exist

► New products► New technology

► Involves intuition, experience► e.g., forecasting sales on

Internet

Qualitative Methods

Forecasting Approaches

► Used when situation is ‘stable’ and historical data exist

► Existing products► Current technology

► Involves mathematical techniques

► e.g., forecasting sales of color televisions

Quantitative Methods

Demand Management

A

B(4) C(2)

D(2) E(1) D(3) F(2)

Dependent Demand:Raw Materials, Component parts,Sub-assemblies, etc.

Independent Demand:Finished Goods

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Components of Demand

Average demand for a period of time

TrendSeasonal elementCyclical elementsRandom variationAutocorrelation

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Finding Components of Demand

1 2 3 4

x

x xx

xx

x xx

xx x x x

xxxxxx x x

xx

x x xx

xx

xx

x

xx

xx

xx

xx

xx

xx

x

x

Year

Sale

s

Seasonal variation

LinearTrend

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Types of Forecasts

Qualitative (Judgmental)

Quantitative Time Series Analysis Causal Relationships Simulation

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Qualitative Methods

Grass Roots

Market Research

Panel Consensus

Executive Judgment

Historical analogy

Delphi Method

QualitativeMethods

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Delphi Method

l. Choose the experts to participate representing a variety of knowledgeable people in different areas

2. Through a questionnaire (or E-mail), obtain forecasts (and any premises or qualifications for the forecasts) from all participants

3. Summarize the results and redistribute them to the participants along with appropriate new questions

4. Summarize again, refining forecasts and conditions, and again develop new questions

5. Repeat Step 4 as necessary and distribute the final results to all participants

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Time Series Analysis

Time series forecasting models try to predict the future based on past data

You can pick models based on:1. Time horizon to forecast2. Data availability3. Accuracy required4. Size of forecasting budget5. Availability of qualified personnel

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► MA is a series of arithmetic means ► Used if little or no trend► Used often for smoothing

► Provides overall impression of data over time

Moving Average Method

Simple Moving Average Formula

F = A + A + A +...+Ant

t-1 t-2 t-3 t-n

The simple moving average model assumes an average is a good estimator of future behavior

The formula for the simple moving average is:

Ft = Forecast for the coming period N = Number of periods to be averagedA t-1 = Actual occurrence in the past period for up to “n”

periods

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Moving Average Example

MONTH ACTUAL SHED SALES 3-MONTH MOVING AVERAGEJanuary 10

February 12

March 13

April 16

May 19

June 23

July 26

August 30

September 28

October 18

November 16

December 14

(10 + 12 + 13)/3 = 11 2/3

(12 + 13 + 16)/3 = 13 2/3

(13 + 16 + 19)/3 = 16(16 + 19 + 23)/3 = 19 1/3

(19 + 23 + 26)/3 = 22 2/3

(23 + 26 + 30)/3 = 26 1/3

(29 + 30 + 28)/3 = 28

(30 + 28 + 18)/3 = 25 1/3

(28 + 18 + 16)/3 = 20 2/3

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Simple Moving Average Problem (1)

Week Demand1 6502 6783 7204 7855 8596 9207 8508 7589 892

10 92011 78912 844

F = A + A + A +...+Ant

t-1 t-2 t-3 t-n

Question: What are the 3-week and 6-week moving average forecasts for demand?

Assume you only have 3 weeks and 6 weeks of actual demand data for the respective forecasts

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Week Demand 3-Week 6-Week1 6502 6783 7204 785 682.675 859 727.676 920 788.007 850 854.67 768.678 758 876.33 802.009 892 842.67 815.33

10 920 833.33 844.0011 789 856.67 866.5012 844 867.00 854.83

F4=(650+678+720)/3

=682.67F7=(650+678+720 +785+859+920)/6

=768.67

Calculating the moving averages gives us:

©The McGraw-Hill Companies, Inc., 2004

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500550600650700750800850900950

1 2 3 4 5 6 7 8 9 10 11 12

Dem

and

Week

De

Plotting the moving averages and comparing them shows how the lines smooth out to reveal the overall upward trend in this example

Note how the 3-Week is smoother than the Demand, and 6-Week is even smoother

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Simple Moving Average Problem (2) Data

Week Demand1 8202 7753 6804 6555 6206 6007 575

Question: What is the 3 week moving average forecast for this data?

Assume you only have 3 weeks and 5 weeks of actual demand data for the respective forecasts

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Simple Moving Average Problem (2) Solution

Week Demand 3-Week 5-Week1 8202 7753 6804 655 758.335 620 703.336 600 651.67 710.007 575 625.00 666.00

F4=(820+775+680)/3

=758.33F6=(820+775+680 +655+620)/5 =710.00

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► Increasing n smooths the forecast but makes it less sensitive to changes

► Does not forecast trends well► Requires extensive historical data

Potential Problems With Moving Average

► Used when some trend might be present ► Older data usually less important

► Weights based on experience and intuition

Weighted Moving Average

Weighted moving average

Weighted Moving Average

MONTH ACTUAL SHED SALES 3-MONTH WEIGHTED MOVING AVERAGEJanuary 10

February 12

March 13

April 16

May 19

June 23

July 26

August 30

September 28

October 18

November 16

December 14

WEIGHTS APPLIED PERIOD3 Last month

2 Two months ago

1 Three months ago

6 Sum of the weights

Forecast for this month =

3 x Sales last mo. + 2 x Sales 2 mos. ago + 1 x Sales 3 mos. ago

Sum of the weights

[(3 x 13) + (2 x 12) + (10)]/6 = 12 1/6

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Weighted Moving Average

MONTH ACTUAL SHED SALES 3-MONTH WEIGHTED MOVING AVERAGEJanuary 10

February 12

March 13

April 16

May 19

June 23

July 26

August 30

September 28

October 18

November 16

December 14

[(3 x 13) + (2 x 12) + (10)]/6 = 12 1/6

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[(3 x 16) + (2 x 13) + (12)]/6 = 14 1/3

[(3 x 19) + (2 x 16) + (13)]/6 = 17

[(3 x 23) + (2 x 19) + (16)]/6 = 20 1/2

[(3 x 26) + (2 x 23) + (19)]/6 = 23 5/6

[(3 x 30) + (2 x 26) + (23)]/6 = 27 1/2

[(3 x 28) + (2 x 30) + (26)]/6 = 28 1/3

[(3 x 18) + (2 x 28) + (30)]/6 = 23 1/3

[(3 x 16) + (2 x 18) + (28)]/6 = 18 2/3

Weighted Moving Average Formula

F = w A + w A + w A +...+w At 1 t-1 2 t-2 3 t-3 n t-n

w = 1ii=1

n

While the moving average formula implies an equal weight being placed on each value that is being averaged, the weighted moving average permits an unequal weighting on prior time periods

wt = weight given to time period “t” occurrence (weights must add to one)

The formula for the moving average is:

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Weighted Moving Average Problem (1) Data

Weights: t-1 .5t-2 .3t-3 .2

Week Demand1 6502 6783 7204

Question: Given the weekly demand and weights, what is the forecast for the 4th period or Week 4?

Note that the weights place more emphasis on the most recent data, that is time period “t-1”

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Weighted Moving Average Problem (1) Solution

Week Demand Forecast1 6502 6783 7204 693.4

F4 = 0.5(720)+0.3(678)+0.2(650)=693.4

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Weighted Moving Average Problem (2) Data

Weights: t-1 .7t-2 .2t-3 .1

Week Demand1 8202 7753 6804 655

Question: Given the weekly demand information and weights, what is the weighted moving average forecast of the 5th period or week?

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Weighted Moving Average Problem (2) Solution

Week Demand Forecast1 8202 7753 6804 6555 672

F5 = (0.1)(755)+(0.2)(680)+(0.7)(655)= 672

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Exponential Smoothing Model

Premise: The most recent observations might have the highest predictive value

Therefore, we should give more weight to the more recent time periods when forecasting

Ft = Ft-1 + a(At-1 - Ft-1)

constant smoothing Alphaperiod epast t tim in the occurance ActualA

period past time 1in alueForecast vFperiod t timecoming for the lueForcast vaF

:Where

1-t

1-t

t

a

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Exponential Smoothing Problem (1) Data

Week Demand1 8202 7753 6804 6555 7506 8027 7988 6899 775

10

Question: Given the weekly demand data, what are the exponential smoothing forecasts for periods 2-10 using a=0.10 and a=0.60?

Assume F1=D1

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Week Demand 0.1 0.61 820 820.00 820.002 775 820.00 820.003 680 815.50 793.004 655 801.95 725.205 750 787.26 683.086 802 783.53 723.237 798 785.38 770.498 689 786.64 787.009 775 776.88 728.20

10 776.69 756.28

Answer: The respective alphas columns denote the forecast values. Note that you can only forecast one time period into the future.

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Exponential Smoothing Problem (1) Plotting

500550600650700750800850

1 2 3 4 5 6 7 8 9 10

Dem

and

Week

Demand

0.1

0.6

Note how that the smaller alpha results in a smoother line in this example

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Exponential Smoothing Problem (2) Data

Question: What are the exponential smoothing forecasts for periods 2-5 using a =0.5?

Assume F1=D1

Week Demand1 8202 7753 6804 6555

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Exponential Smoothing Problem (2) Solution

Week Demand 0.51 820 820.002 775 820.003 680 797.504 655 738.755 696.88

F1=820+(0.5)(820-820)=820 F3=820+(0.5)(775-820)=797.75

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The MAD Statistic to Determine Forecasting Error

MAD = A - F

n

t tt=1

n

1 MAD 0.8 standard deviation1 standard deviation 1.25 MAD

The ideal MAD is zero which would mean there is no forecasting error

The larger the MAD, the less the accurate the resulting model

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MAD Problem Data

Month Sales Forecast1 220 n/a2 250 2553 210 2054 300 3205 325 315

Question: What is the MAD value given the forecast values in the table below?

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MAD Problem Solution

MAD = A - F

n=

404

= 10t t

t=1

n

Month Sales Forecast Abs Error1 220 n/a2 250 255 53 210 205 54 300 320 205 325 315 10

40

Note that by itself, the MAD only lets us know the mean error in a set of forecasts

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Tracking Signal Formula The Tracking Signal or TS is a measure

that indicates whether the forecast average is keeping pace with any genuine upward or downward changes in demand.

Depending on the number of MAD’s selected, the TS can be used like a quality control chart indicating when the model is generating too much error in its forecasts.

The TS formula is:

TS =RSFEMAD

=Running sum of forecast errors

Mean absolute deviation

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Simple Linear Regression Model

Yt = a + bx0 1 2 3 4 5 x (Time)

YThe simple linear regression model seeks to fit a line through various data over time

Is the linear regression model

a

Yt is the regressed forecast value or dependent variable in the model, a is the intercept value of the the regression line, and b is similar to the slope of the regression line. However, since it is calculated with the variability of the data in mind, its formulation is not as straight forward as our usual notion of slope.

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Simple Linear Regression Formulas for Calculating “a” and “b”

a = y - bx

b = xy - n(y)(x)x - n(x2 2

)

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Simple Linear Regression Problem Data

Week Sales1 1502 1573 1624 1665 177

Question: Given the data below, what is the simple linear regression model that can be used to predict sales in future weeks?

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Week Week*Week Sales Week*Sales1 1 150 1502 4 157 3143 9 162 4864 16 166 6645 25 177 8853 55 162.4 2499

Average Sum Average Sum

b =xy - n(y)(x)x - n(x

=2499 - 5(162.4)(3)

=

a = y - bx = 162.4 - (6.3)(3) =

2 2

) ( )55 5 9

6310

6.3

143.5

Answer: First, using the linear regression formulas, we can compute “a” and “b”

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Yt = 143.5 + 6.3x

180

Period

135140145150155160165170175

1 2 3 4 5

Sale

s SalesForecast

The resulting regression model is:Now if we plot the regression generated forecasts against the actual sales we obtain the following chart: